The dynamic forces induced during rhythmic human jumping are important in multiple domains, including structural safety, sports performance optimization, and biomechanical research. This work proposes a mathematical model to replicate the vertical dynamic forces induced during rhythmic human jumping on a rigid floor. The jumping motion of a person is modeled using a one-degree-of-freedom nonlinear self-sustained oscillator. This oscillator should be capable of capturing three key phenomena observed experimentally: (1) the vertical jumping force history is approximately periodic, (2) the presence of a stable limit cycle, and (3) self-sustained motion, meaning the jumper (oscillator) produces the required input energy to maintain its motion. The developed oscillator is in the form of a modified hybrid Van der Pol-Duffing (MHVD) system, incorporating two nonlinear inertia terms to fulfill these criteria. The force acting in the vertical direction is expressed through the restoring force of the MHVD oscillator. Analytical solutions for this oscillator are subsequently obtained using an energy-based approach and the Krylov–Bogoliubov method of perturbation. Moreover, the optimal model's parameters have been estimated using the genetic algorithm and experimental data of force signals. The stability of the model parameter is evaluated using bootstrapping with increasing ensemble sizes. Finally, the high coefficient of determination ( R^2 = 0.97 ) indicates that the model-generated signals are in strong agreement with the experimental signals. The validated model enables engineers to predict human-induced loading accurately for vibration serviceability assessment of structures while providing sports scientists and biomechanics researchers with tools for performance analysis and movement optimization.

Pipelines for fluid conveyance are widely employed across a range of engineering applications, including petrochemical plants, natural gas plants, nuclear power stations, water treatment plants and subsea systems. However, unexpected vibrations from various sources can compromise their operational performance and cause damage to the systems. Among piping systems, the pipe-in-pipe (PIP) system is ubiquitous, offering the benefits of thermal insulation and reduced vibration levels. Thus, this study investigates a non-compliant viscoelastic PIP system subjected to harmonic excitation, focusing on vibration analysis and its control. Modelling employs Euler–Bernoulli beam theory, with the dynamic equations derived using the Galerkin method. Initially, optimal centralizer locations are determined to minimize the system amplitude. A comparison between the use of a linear and Duffing nonlinear centralizers is also studied. A nonlinear energy sink (NES) is then integrated into the system, whose optimal stiffness and damping properties for a given mass are determined using an optimization technique. Additionally, some improvement in the nonlinear responses at higher excitation amplitudes has also occurred for a range of NES parameters. It reduces the first resonant peak of the outer pipe as well as the inner pipe in broader frequency range than linear vibration absorber. It is observed that increasing NES stiffness and mass enhances the unstable band and resonant peaks, while higher damping reduces the unstable band of the steady-state responses. The study concludes that the NES application is promising, particularly for attenuating vibrations in the outer pipe and whole system stability.

This study examines the mechanical and microstructural integrity of a pulsed gas metal arc welded (P-GMAW) joint between IN718 and ASS304L, fabricated using ERNiCr-3 filler. The microstructural investigation was examined by means of optical microscopy (OM) and scanning electron microscopy (SEM) provided with energy dispersive spectroscopy (EDS). The SEM/EDS depicts the existence of the Nb (NbC), Ti (TiC), and Cr (Cr23C6) enriched carbides precipitates over the various weld regions, which is confirmed by X-ray diffraction (XRD). These phases, particularly in interdendritic regions, are known to impact the mechanical performance of the weld joint. Additionally, SEM/EDS examined elemental analysis depicting the subsistence of the brittle laves phases in the weld zones. The weld metals microstructure exhibited a transition from columnar and equiaxed dendritic morphology near the weld interfaces and at the weld center, respectively explaining the consequence of the weld temperature gradients in the different regions of the weld area. The results depict that P-GMAW significantly refines the microstructure, reducing the microsegregation of alloying elements, primarily Nb and Ti, thereby improving mechanical properties. P-GMAW welds exhibited excellent tensile strength (664 MPa), superior elongation (39

Elastomers' hyperelastic properties make them popular for mitigating vibration and shock in a variety of engineering applications. These properties are commonly modeled using hyperelastic models, which require the determination of material constants. In the conventional approach, multiple material test data, such as uniaxial, biaxial, planar, and volumetric data, of each material are required to obtain material constants of a hyperelastic model. Elastomer experimental testing is an expensive and time-consuming procedure. These limitations prompt the development of neural networks that can accurately determine the hyperelastic constants without requiring multiple tests. Therefore, this study focuses on developing a deep neural network (DNN) to determine the material constants of the Ogden third-order model for elastomers. Finite element analyses of uniaxial tension and compression tests are performed using ABAQUS software for randomly generated samples to generate a dataset for training the DNN model. The designed DNN model consists of three hidden layers with tanh activation functions and is trained using the AdamW optimizer. The trained DNN model is validated for hydrogenated nitrile butadiene rubber, polychloroprene rubber, and natural rubber (NR) under uniaxial conditions, and for neoprene and silicone rubbers under uniaxial, planar, and O-ring multi-contact tests. Furthermore, simulation responses using DNN-predicted constants for neoprene rubber at 50 °C and 80 °C closely match the experimental data. Additionally, simulation responses with DNN-predicted constants and experimental data for a shock test case study on NR dampers exhibit close agreement. Thus, the proposed DNN model can determine material constants of the hyperelastic model for any kind of rubber using direct component uniaxial data, eliminating the need for coupon tests.

This paper introduces a modified Fourier model for accurately simulating the induced stochastic dynamic jumping force exerted by an individual during jumping motion on a rigid floor. The contact ratio, pace frequency, and amplification factor are the critical parameters in the force modeling. These parameters are considered as random variables. The mean, standard deviation, and interval of variation for the parameters have been computed based on experimental records of individual jumping force-time history. Correlation analysis indicates that the pace frequency and the contact ratio are weakly dependent variables. Moreover, analysis of experimental data shows that the amplification factor depends on both the contact ratio and pacing frequency. To account for this, the modified amplification factor has been incorporated into a truncated Fourier series to model the continuous rhythmic jumping force. The bootstrap resampling technique has been utilized to capture the inherent randomness in the jumping force. Additionally, successive corrections, in terms of the time difference between the metronome beat frequency and the achieved jumping frequency, have been applied in each load cycle to produce the jumping force. Comparisons between the measured force signals and the model-generated forces demonstrate strong agreement. Finally, the jumping vandal loading is simulated on a steel floor in a finite element model, and the responses for both, i.e., the model and the experimental forces, are compared. The results demonstrate that the proposed jumping force model is simple and can be easily used for the vibration serviceability assessment of structures.

Military ships carry sensitive articles and equipment that experience shock loads caused by underwater explosions in the vicinity of the ship. Unwanted shock loads of this kind have the potential to damage extremely energetic objects and compromise the accuracy of extremely delicate machinery. This research aims to perform a finite element (FE) analysis of ring-shaped hydrogenated nitrile butadiene rubber (HNBR) and Sorbothane isolators to protect a sensitive article stored inside a cylindrical-shaped component of a naval ship using ABAQUS. These materials have nonlinear elastic and viscous properties, which are modeled in the ship component’s FE model by the third-order Ogden and generalized Maxwell models, respectively. The material constants of these models are determined using the experimental test data of HNBR and Sorbothane. A transverse shock with a peak amplitude of 60 g is applied at the outer surface of the component, and responses are measured in the form of acceleration of the article, deformation, and stress distribution in the isolators. The proposed HNBR and Sorbothane isolators of considered length provide 97.16

PurposeThis paper aims to design a novel isolation system based on natural rubber (NR), polyurethane (PU), and Sorbothane for protecting a sensitive article kept within a naval vessel container (NVC) from a shock load.MethodsFirst, NVC is analyzed using the MATLAB tool as an analytical model with two degrees of freedom, wherein the elastomer's isolation system is modeled by nonlinear stiffness up to third-order and linear damping. The genetic algorithm determines optimal values of stiffness and damping parameters to minimize simultaneously both the maximum shock transfer to the sensitive article and the maximum deformation of the isolation system. Furthermore, the NVC's 3D finite element model (FEM) is created in ABAQUS and exposed to the transverse shock load to perform an in-depth dynamic analysis of the isolation system. In the 3D FEM, the nonlinear elastic and time-dependent properties of the considered materials are defined based on test data using appropriate hyperelastic and viscoelastic models, respectively.ResultsThe 3D FEM results show that three isolators with lengths of 170 mm, 75 mm, and 500 mm each for NR, PU, and Sorbothane materials, respectively, are optimal. The NVC's 3D simulation results for the optimal design of NR, PU, and Sorbothane isolators closely match the analytical model's optimized results.ConclusionsMoreover, the shock is reduced by 98.26%, 98.29%, and 98.49%, respectively, for NR, PU, and Sorbothane isolators with the maximum deformation of isolators below 10 mm, demonstrating the high effectiveness of the proposed design in shock mitigation.

Understanding and controlling pipe vibrations are of key concern as they affect the serviceability and performance of pipeline systems. A novel metamaterial concept can be exploited to control these vibrations. In this article, propagation characteristics of flexural waves in a pipe coupled with rack are investigated. The dispersion relation, which corelates the propagation constant with frequency is obtained using the transfer matrix method in conjunction with Bloch's theorem. The results reveal the existence of multiple wide passbands in the low frequency range. These propagation characteristics are verified using a finite element model. The emergence of these multiple passbands is attributed to various bending modes of the pipe, and it is necessary to efficiently control them. In order to achieve both independent and simultaneous control of multiple passbands, the feasibility of deploying either a single or a two degree of freedom resonator at each span of the pipe is evaluated. As the positioning of resonators within a span governs their performance, to gain a deeper understanding of this, an iterative procedure is adopted wherein resonators are placed at each possible location in the span. A genetic algorithm-based optimization is then performed to arrive at the corresponding optimal parameters. The ideal location for placing a resonator to control each passband is the one that yields the best performance. Finally, the efficacy of the proposed control scheme is verified using Gaussian white noise as input. The dispersion relation and control schemes proposed herein not only provide insights into understanding the propagation behavior of flexural wave and their control in pipes, but also can be equally applied to other analogous periodic structures.

Periodic structures possess frequency bandgaps wherein the waves cannot pass through. Here, the propagation behaviour of vertical and lateral flexural waves and its control in a railway track supported on periodic sleeper blocks connected using fasteners is investigated. The dispersion relationships for two kinds of waves are derived through Floquet–Bloch theorem, and the ensuing band structures are validated from finite element (FE) models. The results demonstrate that a Bragg and a locally resonant (LR) bandgap evolve in the track for both types of waves in the examined frequency range. However, the bandwidth of these bandgaps is found to be very small. Thus, waves can freely propagate in the track for a large frequency range, causing vibration and noise. Subsequently, the dependence of transmission properties of waves on the number of unit cells is studied. It is observed that the attenuation in the bandgap is significantly improved on increasing the number of unit cells. Further, to tune the bandgap properties, a single-degree-of-freedom resonator (SDoF) is used in the middle of each unit cell of the track. Afterwards, the parametric influence of resonator properties, that is, mass, stiffness and damping, on bandgaps is investigated in depth. Moreover, the phenomenon of bandgaps coupling is demonstrated when the resonator is tuned near the Bragg bandgap. The results provided herein are promising to realize the characteristics of flexural waves and to design resonators for track structures.

In naval engineering, protecting sensitive articles from shock loads is a major concern, as it may lead to adverse consequences. This paper focuses on the design of a novel Hydrogenated Nitrile Butadiene Rubber (HNBR) and Polychloroprene Rubber (PCR)-based shock isolation system to protect a sensitive article stored in a hollow cylindrical naval vessel container (NVC). Firstly, NVC is modeled as a two-degree-of-freedom lumped parameter model (LPM), wherein isolators made of HNBR and PCR materials are modeled with 5-order polynomial nonlinear stiffness and linear damping. The optimal values of the isolator parameters are obtained using a multi-objective genetic algorithm, and corresponding responses to a shock load are found using MATLAB. Furthermore, a three-dimensional (3D) finite element model (FEM) of the NVC is generated in ABAQUS and subjected to shock loading in a transverse direction to conduct a comprehensive dynamic analysis of the isolation system. In 3D simulation, HNBR and PCR materials are modeled using a hyper-viscoelastic model developed based on experimental test data. The 3D simulation results of the NVC for the optimized design of HNBR and PCR isolators agree with the optimized results of the LPM. Moreover, the proposed HNBR and PCR isolators are very effective in shock reduction.

Composite plates find extensive use in aerospace and marine industries due to light weight, high strength-to-weight ratio and large stiffness. Their stiffness or natural frequency changes due to variation in environmental conditions such as temperature and moisture, and thus their dynamic performance can be adversely affected. Therefore, a nonlinear energy sink (NES) based vibration absorber is proposed that remains effective in a wide range of frequency change. A cantilever composite laminated plate (CCLP) is modelled using classical laminate plate theory. Moreover, dynamics of the plate-NES system is expressed by Euler–Lagrange equation; discretized in two fixed-free and two free-free modes using the Galerkin method. As the free end is more prone to vibration under excitation, first two resonant peaks in free-free direction of the plate are extensively studied in hygrothermal environment- with and without NES. The particle swarm optimization is used to optimize the NES parameters. Numerical analysis shows that the optimal NES decreases the first mode’s peak amplitude by about 70

Flexural vibration characteristics of a meta-pipe are investigated in this paper. Initially, the metamaterial piping system consisting of a homogeneous pipe and periodic flexible supports is designed. Subsequently, the dispersion relationship which is a function of the wavenumber and the frequency is derived employing the transfer matrix method and Bloch’s theorem. The designed system reveals a zero-frequency stopband and a wide passband in the examined frequency range, which are verified by both experimental and numerical results. To enhance the performance of this system, it is essential to effectively control the obtained passband. For this, a single-degree-of-freedom localized resonator is designed, which is subsequently installed at the center of each unit-cell of the pipe. The dispersion properties of this system are first evaluated analytically and then validated using experimental and numerical methods. Finally, the effect of pipe system parameters and resonator properties on the stopband characteristics is studied in depth. It was observed that the stopband properties can be effectively tuned by appropriately designing the piping system and resonators. The results presented in this study offer valuable insights into the propagation characteristics of flexural waves and the strategies devised for controlling vibrations in pipes.

This paper proposed a single-degree-of-freedom self-sustained nonlinear oscillator capable of precisely predicting the bouncing force induced by a person during bouncing activity on a flat and rigid surface. A bouncing person produces essential internal energy required to maintain its motion, so it can be modeled as a self-sustained oscillator that can generate (i) the stable limit cycle, (ii) the periodic bouncing force signal, and (iii) the self-sustained motion. A hybrid Van der Pol-Rayleigh oscillator added with two quadratic and one cubic nonlinear terms has been derived to yield desired softening and hardening effects as well as even and odd harmonics, as observed from the analysis of experimental bouncing force data. The force applied on the surface corresponds to its restoring force. The stability analysis of the oscillator has been performed using the energy balance and perturbation methods. The model parameters are extracted from the experimental bouncing force data resulting from a bouncing test on a group of seven subjects with shoe insoles at six different frequencies guided by a metronome. The bootstrapping method has been performed to examine the convergence of mean values of each model parameter by increasing the cardinality of the experimental set. The bouncing force signals produced by the proposed model and experimental results demonstrate an excellent agreement.

Elastomer materials are widely used as shock absorbers in a variety of practical applications including the automotive, aerospace, marine industries and structures. The straightforward Hooke's law is insufficient to adequately describe the behavior of elastomeric materials due to their nonlinear elastic and viscous properties. This study proposes a hyper-viscoelastic model to describe the mechanical behavior of Hydrogenated Nitrile Butadiene Rubber (HNBR) 62 Duro shore A and Polychloroprene Rubber (PCR) 55 Duro shore A. Six distinct hyperelastic models-Yeoh, Rivlin, Arruda-Boyce, Mooney-Rivlin, Neo-Hookean, and Ogden- are compared herein to explain the nonlinear elastic behavior of elastomers. While the time-dependent characteristics of the considered materials have been described using the four parameters Generalised Maxwell (GM) model. The material parameters of models are determined using the least square fit (LSF) optimization algorithm from the uniaxial, planar, and stress relaxation test data. The stability and suitability of each hyperelastic model is assessed using the Drucker stability. The accuracy of each model is represented by Root Mean Square Error (RMSE) of curve fitting between theoretical and experimental data. On this basis, the Ogden order three (N = 3) model and the four-parameter GM models are selected which well agreed with the experimental test data and they are integrated to generate the hyper-viscoelastic constitutive model. In addition, the hyper-viscoelastic model is used to simulate the HNBR and PCR dampers under shock load. The numerically generated response is finally compared with the experimental test result of natural rubber (NR) 60 IRH from the existing literature to confirm accuracy of the proposed model.

Unbalance in rotating components is very common. Moreover, rotating components input a force to the supporting structure whose amplitude varies quadratically with the rotor speed. As a rotating machine starts from the static condition and approaches to a higher operating speed, it is possible that several modal frequencies of the support beam get excited. Therefore, a vibration mitigation system is required to be efficient at higher operating speeds as well as to provide enough suppression at lower traversing speeds. Here, a nonlinear energy sink (NES) is attached underneath a simply supported beam subjected to the vertical unbalance force component of the rotor. Euler-Bernoulli beam theory is used for the dynamic modeling of the beam along with the Euler-Lagrange equation to get equations of motion of the beam and NES, which are solved numerically. The complexification averaging method is utilized to get the amplitude-frequency response of the system analytically for stability analysis and comparison with the numerical solution. The optimum values of the absorber parameters are obtained utilizing particle swarm optimization. The optimum NES is capable of efficiently reducing vibration amplitude for several modes of beam excited at different rotor speeds. It is found that the NES tuned at the first mode is effective in amplitude reduction for lower to higher operating speed ranges, whereas the NES tuned at the third mode performs better for higher operating speeds. The optimum NES also performs well for a sufficient range of change in the amount of unbalance of the rotor.

Vibrations generated from the passage of trains including that from metros often get transmitted to the adjacent structures including buildings. This problem is particularly serious in cities wherein the resulting vibrations can either cause structural issues or can lead to serious discomfort for the occupants. Also, wheel–rail interaction often produces unwanted noise which can affect the inhabitants of the buildings near to these tracks. Understanding the propagation behavior of vibrations in the rail and thereby to the adjacent structures is essential in order to efficiently control them. Thus, the propagation behavior of flexural wave in a typical rail is analyzed in the context of Floquet–Bloch theorem for periodic structures. The ensuing dispersion relations are validated using finite element models. Subsequently, two-degrees-of-freedom resonators are coupled with rail to tune the stop band characteristics. The targeted frequency ranges in the considered pass band are very efficiently controlled using these resonators. Further, the efficacy of this control strategy is assessed using a random Gaussian white noise loading in the time domain and comparing the resulting vibration transmission characteristics from the original rail with that of the rail embedded with the proposed resonators. This study helps to realize the propagation characteristics of flexural waves in rails and the design of passive control mechanisms to reduce the transmission of the resulting vibrations.

Purpose Composite sandwich structures are becoming an essential part of engineering appliances due to their excellent mechanical and structural properties, high strength-to-weight as well as stiffness-to-weight ratios. And so, they are widely used in aerospace and marine applications, such as airplane wings, flight control surfaces, turbine blades, ship interiors, and small boats and yachts. Despite their superior properties, the sandwich plates consisting of an aluminum core and carbon fiber-reinforced plastic face sheets exhibit low-frequency resonant modes when subjected to external excitation. Therefore, in this paper, a nonlinear energy sink (NES) is attached to the thermally induced sandwich plate to attenuate the resonant peaks passively in a broad frequency range. Methods The equation of motion of the sandwich plate-NES system is obtained by utilizing Lagrange Euler’s equation followed by Galerkin discretization. The analytical solution of the system is obtained by the complexification averaging method and arc-length continuation method. The nonlinear and stability analyses are also conducted for the present system. Results The results show that an optimum NES obtained by the sensitivity analysis of the response curve attenuates the resonant peaks effectively and is applicable in a wide frequency range at various temperatures. Conclusion Optimum parameters and the location of the NES help to eliminate the complex nonlinear dynamical phenomena at the first resonance frequency in various thermal environments.

A two-degree-of-freedom (TDOF) nonlinear energy sink (NES) is proposed to suppress the vibration of a simply supported beam subjected to a large amplitude excitation corresponding to its fundamental frequency. The Euler–Bernoulli beam theory along with the Euler–Lagrange equation is utilized for the dynamical modeling of the beam-NES system. The numerical solutions are compared with an approximate analytical solution based on the complexification-averaging method. As the beam response significantly depends on the values of the NES parameters, the optimal values are obtained by employing the particle swarm optimization. After comparison with a single-degree-of-freedom (SDOF) NES, it is found that at lower excitation amplitude SDOF NES is more effective than TDOF NES, however, as the excitation amplitude increases, the TDOF NES gets more effective in terms of resonant peak suppression and energy dissipation. The TDOF NES reduces the first peak amplitude of about 95